The edge current, in turn, emits electromagnetic waves with the frequency \(2\omega \)  and the vector potential \(\mathbf {A}_{2\omega }(\mathbf {r}, t) = \mathbf {A}_{2\omega }(\mathbf {r}) \mathrm {e}^{-2\mathrm {i}\omega t} + \mathbf {A}_{2\omega }^*(\mathbf {r}) \mathrm {e}^{2\mathrm {i}\omega t}\) . The field \(\mathbf {A}_{2\omega }(\mathbf {r})\)  can be found from the wave equation [1]}
\(\Delta \mathbf {A}_{2\omega } + k_{2\omega }^2 \mathbf {A}_{2\omega } = -\frac{4\pi }{c} \mathbf {j}_{2\omega }(x) \delta (z)\:,\) 
